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Semenov [28]
4 years ago
14

Ahmed and Karnia are building scenery of the Egyptian pyramids out of plywood for a community play. They pyramids are represente

d by triangles on a rectangular base
A.) how many square feet of plywood is in the scenery? Show your work

B.) the pyramids (the triangles) will be painted gray, and the base(the rectangle) will be painted black. How much of each paint color will they use, if one quart covers 45 square feet? Only one side of the model needs to be painted, but two coats of paint will be needed. Show your work. Round to the nearest hundredth of a square foot

Mathematics
1 answer:
Arlecino [84]4 years ago
5 0
A.)
 
The first thing we must do for this case is to find the area of ​​the complete figure.
 We have then:
 Triangle 1:
 A1 = (1/2) * (1.5) * (1)
 A1 = 0.75 feet ^ 2
 Triangle 2:
 A2 = (1/2) * (1.5) * (2)
 A2 = 1.5 feet ^ 2
 Triangle 3:
 A3 = (1/2) * (0.75) * (1)
 A3 = 0.375 feet ^ 2
 Rectangle:
 A4 = (5) * (0.75)
 A4 = 3.75 feet ^ 2
 Adding the areas we have:
 A = A1 + A2 + A3 + A4
 A = 0.75 + 1.5 + 0.375 + 3.75
 A = 6.375 feet ^ 2
 Answer:
 there are 6,375 feet ^ 2 of plywood in the scenery

 B.)
 
Triangles:
 A = A1 + A2 + A3
 A = 0.75 + 1.5 + 0.375
 A = 2,625 feet ^ 2
 Two layers of paint:
 A = 5.25 feet ^ 2 <45 feet ^ 2
 Rectangle:
 A = 3.75 feet ^ 2
 Two layers of paint:
 A = 7.5 feet ^ 2 <45 feet ^ 2
 Answer:
 
One quart of each color is needed.
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a.) A flat pattern that could be folded to make a 3-dimensional figure is called a "net." You can draw one for Tyler's bench by picking any surface of that rectangular prism and making a drawing of it. At any edge you choose, you can add the adjacent surface to your drawing. Keep doing this until all 6 surfaces are shown in their correct relationship to adjacent surfaces. An example is attached. (This is not the only way the net can be drawn.)

Interior lines of the net can be solid or dashed as you wish. I have shown some of them dashed so as to better illustrate how the area can be computed.

b.) The area of this figure represents the surface area of the rectangular prism. The dimensions of each surface will be 1×1.5, 1×5, or 1.5×5. There are two surfaces with each pair of dimensions. (Perhaps you can find each of these rectangles on the net diagram. Ones with the same dimensions are opposite faces of the rectangular prism.) We can add up the areas of the smaller rectangles to find the total, or we can take advantage of the drawing and divide the area into a smaller number of larger chunks that may make the computation easier.

For example, the rectangle AI that is shaded red is 5×4 in size, for a total of 20 ft². The rectangle KN that is shaded green is 8×1 in size, for a total of 8 ft². Then the total amount of cloth Tyler needs to reupholster his bench is

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